Question

9) For a vibrating system as shown in Figure 8, the mass m = 80 kg, spring constant is k = 85 kN/m, damping coefficient c = 4580 N.s/m and frequency f = 7 Hz. (a) Draw the free body diagram of the system. (b) Write the equation of motion using Lagrangian mechanics and Newtonian mechanics. (c) Determine the natural frequency, frequency ratio and damping ratio of the system.

          9) For a vibrating system as shown in Figure 8, the mass m = 80 kg, spring constant is k = 85 kN/m, damping coefficient c = 4580 N.s/m and frequency f = 7 Hz.
(a) Draw the free body diagram of the system.
(b) Write the equation of motion using Lagrangian mechanics and Newtonian mechanics.
(c) Determine the natural frequency, frequency ratio and damping ratio of the system.

9) For a vibrating system as shown in Figure 8, the mass m = 80 kg, spring constant is k = 85 kN/m, damping coefficient c = 4580 N.s/m and frequency f = 7 Hz.
(a) Draw the free body diagram of the system.
(b) Write the equation of motion using Lagrangian mechanics and Newtonian mechanics.
(c) Determine the natural frequency, frequency ratio and damping ratio of the system.

Added by Raul A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

06/16/2023

Step 1

- Consider the mass \( m \) as a block. - Draw the spring \( k \) attached to one side of the mass and anchored at the other end to a fixed support. - Draw the damper \( c \) parallel to the spring, also attached to the mass and anchored to a fixed Show more…

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